[HTML][HTML] A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

MA Eltaher, ME Khater, SA Emam - Applied Mathematical Modelling, 2016 - Elsevier
The enabling emerging technologies such as nanotechnology increased the demand for
small-size devices. The proper understanding of the nonclassical behavior of nanostructures …

A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration

M Aydogdu - Physica E: Low-dimensional Systems and …, 2009 - Elsevier
In the present study, a generalized nonlocal beam theory is proposed to study bending,
buckling and free vibration of nanobeams. Nonlocal constitutive equations of Eringen are …

[HTML][HTML] Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

Ö Civalek, Ç Demir - Applied Mathematical Modelling, 2011 - Elsevier
In this paper, elastic beam model using nonlocal elasticity theory is developed for the
bending analysis of microtubules (MTs) based on the Euler–Bernoulli beam theory. The size …

A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method

Ö Civalek, C Demir - Applied Mathematics and Computation, 2016 - Elsevier
A simple nonlocal beam model is proposed to study buckling response of protein
microtubules. The size-effect for buckling model of microtubules is considered by using the …

Axial vibration of the nanorods with the nonlocal continuum rod model

M Aydogdu - Physica E: Low-dimensional Systems and …, 2009 - Elsevier
Nonlocal elastic rod model is developed and applied to investigate the small-scale effect on
axial vibration of nanorods. Explicit expressions are derived for frequencies for clamped …

Recent researches on nonlocal elasticity theory in the vibration of carbon nanotubes using beam models: a review

L Behera, S Chakraverty - Archives of Computational Methods in …, 2017 - Springer
Understanding dynamic behavior of carbon nanotubes has been of interest to researchers
because of its practical applications. Recent studies show that nonlocal elasticity theory …

Levy type solution method for vibration and buckling of nanoplates using nonlocal elasticity theory

T Aksencer, M Aydogdu - Physica E: Low-dimensional Systems and …, 2011 - Elsevier
In the present study, buckling and vibration of nanoplates are studied using nonlocal
elasticity theory. Navier type solution is used for simply supported plates and Levy type …

Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory

J Yang, LL Ke, S Kitipornchai - Physica E: Low-dimensional Systems and …, 2010 - Elsevier
Nonlinear free vibration of single-walled carbon nanotubes (SWCNTs) is studied in this
paper based on von Kármán geometric nonlinearity and Eringen's nonlocal elasticity theory …

[HTML][HTML] Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models

C Demir, Ö Civalek - Applied Mathematical Modelling, 2013 - Elsevier
In this paper, the size-effects in the torsional and axial response of microtubules by using the
nonlocal continuum rod model is investigated. To this end, continuous and discrete rod …

Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method

M Danesh, A Farajpour, M Mohammadi - Mechanics Research …, 2012 - Elsevier
The small scale effect on the axial vibration of a tapered nanorod is studied employing
nonlocal elasticity theory. The nonlocal elasticity theory is used to analyze the mechanical …